Precipitations of Forms

by Daniel Ranard

Wandereryou cannot
turn around in
the Absolute: there are no entrances or exits
no precipitations of forms
to use like tongs against the formless

—A.R. Ammons, in Guide

The world is usually grasped by its pieces. We may speak of a “holistic” perspective, but it's hard to understand all of a thing at once, or even to talk about it all at once. So we delineate pieces within the whole; we analyze the pieces and their interactions. For instance, to understand the recent political changes in the United States, it is uninformative to treat society monolithically. On the other hand, it's impossible to consider the disparate lives of every citizen at once. Instead, we delineate groups within the whole of society – political groups, racial groups, geographic groups – and discuss their interplay. Some delineations are more useful than others; it's probably difficult to understand the 2016 election in terms of cat- and dog-lovers. And all delineations share some degree of blurriness or arbitrariness: race is already a blurry construction, and though it may be crystallized in a bureaucratic form, the distinction only makes it more arbitrary. Through these delineations, we come to understand the otherwise formless and chaotic world and even to create our experience within it.

Imagine viewing all of human history as a video on fast-forward; observed all at once, you see only the tangled scurrying human beings. You cannot usefully describe what you see, nor guess what might happen next. But to the historian, history is not formless, though it may require hard work and ingenuity to find the right units of analysis. The traditional divisions of global society into self-described nation states and political institutions may serve you well, but new divisions may also be informative. In What is Global History?, Sebastian Conrad outlines the view that historians must not “accept political entities a priori as the boundaries of analysis, but instead trace the actual scope of entanglements and interconnections and work form there.” For instance, Marx chose to analyze history as an interplay of social classes. New perspectives might require more than the simple re-organization of people into different groups; historians might also invent new abstractions, such as the concept of capital, that help organize their observations.

These abstractions can be world-changing and world-making. That is, we live in the world of our chosen abstractions, which shape our narratives about ourselves and society. Although we choose these delineations and abstractions ourselves, I would not draw the radical conclusion that all choices are equal, or that the world is anything we make of it. Some choices are more useful, or maybe also more true or beautiful.

Our vision of the world is mutable, and we may find certain re-envisionings superior. For example, it is difficult to characterize the minds of animals, or to specify the qualities of their unfamiliar mental life. You might abstract certain behaviors like “reasoning,” in order to distinguish creatures that reason and creatures that do not. Meanwhile, Jeremy Bentham suggested a different delineation, over 200 years ago: “The question is not, can [animals] reason? Nor, can they talk? But, can they suffer?” Our envisioning of an ethical world hinges on the abstractions we use to understand the minds of animals, and how they map onto the abstractions we use to describe ourselves.

While it's easy to imagine that the ethical or political dimensions of our world allow for changing delineations and the crystallization of new abstractions, our scientific descriptions of the physical world appear more rigid and objective. To understand the material world does not seem to require a “precipitation of forms,” to borrow a phrase from the poet A.R. Ammons, because the fundamental physical forms are already manifest: the elementary particles of the Standard Model, or the well-tabulated elements of the periodic table. However, just like historians watching collections of humans scurry through history, physicists try to make broader sense of their own subjects, namely the collections of particles that constitute the world. Even though physicists understand the rules for how particles interact, it's computationally difficult to calculate how they behave in the aggregate, and their collective behavior may appear unintelligible. The task of understanding is made easier by certain organizing abstractions: for instance, we group certain clusters of atoms into “objects,” like molecules or even rocks and trees, whose interactions may be analyzed more fruitfully. The question of how to intelligently divide the world into objects may appear obvious for human-scale systems on Earth. But it's less obvious when pondering, say, the violent surface of the sun. Nonetheless, the identification of objects like magneto-hydrodynamic currents renders intelligible what is otherwise absolute chaos.

Often, the “precipitation of forms” in physics is more drastic than conceptually dividing a collection of atoms into usefully defined clusters. In a sense, the use of three Cartesian coordinates to describe space is already an imposition of form upon the formless. With a certain choice of axes, the points of physical space suddenly acquire three labels, (x, y, z). Some choices of coordinates prove more useful than others. Even the labeling of physical space with three dimensions (as opposed to more or fewer) is a choice we make, not taken for granted in modern theoretical physics. To see why, let's first consider Conway's “Game of Life,” an imagined world with simple rules. Conway's world is made up of an infinite two-dimensional grid of squares, like graph paper. Some squares are filled in black; some are white. Each second, the squares change color based on the color of their neighboring squares, according to a straightforward rule. (The magical part is that, depending on the initial filling of the squares, sometimes little “creatures” appear that reproduce and interact.) Even if you didn't know the rules that Conway invented, they would become apparent if you carefully studied a video of Conway's world.

Now imagine that we take all the squares and re-arrange them in a one-dimensional chain. In particular, imagine that the squares still change color based on the color of their old neighbors – their neighbors on the two-dimensional grid – even though they are now arranged in a single chain. If you watched a video of this one-dimensional world, it would be extremely difficult to recognize the governing rules. You would need to realize that, actually, “this square in the chain changes color based on that square very far away,” and so on. But an ingenious physicist studying the chain world would eventually realize that the physics is much easier described if one abstractly re-arranges the squares into a two-dimensional grid. Conceived abstractly in two dimensions, the world would finally make sense, and one could even identify Conway's creatures.

A world with the Game of Life played in one dimension may seem exotic, but we can find a similar example much closer to home. That is, we can find an example of physical matter whose behavior is best understood through a radical re-interpretation of the system, a precipitation of unexpected forms. Consider your computer when it runs a simulation of the Game of Life. If asked what your computer is “doing,” you might assert that it's running the Game of Life. Even if you shut off the screen, you would assert the same. (If you turned the screen back on ten minutes later, it would become apparent that the computer had indeed been running the simulation.) On the other hand, we can imagine a physicist who hasn't ever seen a computer, who we ask to briefly examine the interior of the computer while the screen is shut off. When we ask what's going on, he reports there are electrons following silicon tracks. “They're just following the rules of electromagnetism,” he says. If we asked him to calculate how the electrons will be distributed in ten minutes from now, he would complain that the calculation is nearly impossible. But with an unlikely stroke of genius, he might develop many layers of abstraction, ultimately recognizing that the motion of the electrons corresponds, in some complicated way, to Conway's rules on an imagined grid. The physicist might even say that the computer is an instance of Conway's two-dimensional world. Or, at least, it's both a box filled with circuits and a two-dimensional grid world. If you are willing to believe that the simple creatures present in the Game of Life could evolve to become complex and sentient over the course of the simulation, such creatures would certainly agree that “the computer” – which they would just call “the world” – is in fact structured as a two-dimensional grid following Conway's rules.

Under ordinary circumstances, the creatures in the simulation would know nothing of the underlying computer, so they would not describe their world as such. However, if the simulation admitted certain errors and irregularities that correlated with the physical structure of the computer, then the creatures might begin to modify their theory of physics. Ultimately, their theory of physics might describe a three-dimensional world with a box full of circuits that somehow gives rise to the two-dimensional grid of their more direct experience.

This example may still appear exotic and irrelevant. You may consider the statement that “the computer is also Conway's world” to be trivial semantics, while also rejecting the possible existence of sentient creatures in the simulation who could voice their disagreement. But in some sense, we are the creatures in the simulation. No — I'm not referring to the idea that we live inside the computer simulation of an alien civilization (the crazy idea recently embraced by Neil deGrasse Tyson and Elon Musk). I'm referring to the possibility that the fundamental theory of physics may look very unlike the three-dimensional world we know. Many respected theoretical physicists seriously entertain the idea that the world is best described by a model with a different number of dimensions, governed by very different rules – just like the creatures in the computer simulation of Conway's Game of Life, who are led to speculate about the existence of a three-dimensional world with a box full of circuits. Such a world would not be a different world, but rather a new description of the same world, useful for calculating the behavior of physical matter at the finest level of detail.

Finally, even if the underlying physics of the world is not so exotic, we are still living in a simulation of sorts. The world is made of quarks and electrons, and yet we usually choose to speak in terms of people and trees. Or rather, without privileging the small: the world is equally well made of people and trees. Society is composed of individuals, yet we choose to speak in terms of social class and political factions. We live in an abstraction of our own creation, a world that is constrained by the facts of observation but which permits constant re-envisioning.